Abstract The impact of quadrupole and octupole collectivity in the dynamic of low-lying collective states is discussed for a set of Xe, Ba, Ce and Nd isotopes with neutron numbers 54 ⩽ N ⩽ 96. Mean field based methods including pairing are used in our microscopic description along with the Gogny D1M force. Starting with a set of Hartree–Fock–Bogoliubov constrained states we consider dynamic fluctuations of the collective variables by using the generator coordinate method. Related quantities like reduced electromagnetic transition probabilities B(E1) and B(E3) and negative-parity excitation energies and their behavior with neutron number are discussed and compared with the available experimental data. The coupling between the quadrupole and octupole degrees of freedom is found to be rather weak in all the considered nuclei and therefore the properties of the negative parity states can be reasonably well described in terms of the octupole degree of freedom alone. The results of the calculations point towards dynamically enhanced octupole correlations around the ‘octupole magic’ neutron numbers N = 56 and N = 88.